Matrix Operations

Inverse

Suppose we have to solve the equation $AX=b$ for $b$.

If vector $b$ changes, one has to call np.linalg.solve() over and over. Instead, if $A^{-1}$ were calculated once, matrix multiplication with $b$ could be done over and over, more efficiently, to obtain different solutions.

The inverse of a matrix may be computed with the inv function of the linalg package.

Let’s use the inverse of the matrix to obtain the solution to the problem in the first lesson.

$AX=b$

$A^{-1}AX=A^{-1}b$

$X=A^{-1}b$

If the inverse of matrix A is called Ainv, the solution for the equation may be obtained through matrix multiplication of Ainv with the right-hand side. Let’s look at an implementation of this below.